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Large Free Algebras in the Ring of Fractions of Skew Polynomial Rings
Author(s) -
Shirvani M.,
Gonçalves J. Z.
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007772
Subject(s) - mathematics , polynomial ring , automorphism , skew , rank (graph theory) , ring (chemistry) , pure mathematics , polynomial , quotient ring , quotient , group ring , group (periodic table) , combinatorics , algebra over a field , mathematical analysis , computer science , telecommunications , chemistry , organic chemistry
It is shown that the division ring of quotients of a skew polynomial ring of automorphism type, if infinite‐dimensional over its centre k and satisfying suitable hypotheses, contains the group algebra of a free group of large rank (usually at least ∣ k ∣). The result applies, in particular, to the skew polynomial rings constructed from rational function fields, and affirmatively settles the conjectures of Makar–Limanov and Lichtman in this case.